Gravity is the force of inherent natural attraction between two massive bodies. The magnitude of the gravitational force is directly related to the mass of the bodies and is inversely related to the square of the distance between centers of mass of the two attracted bodies.
Gravity is measured as acceleration, g, usually as a vertical vector component. The freefall acceleration, g, of an object near the surface of the earth is given to a first approximation by the gravitational attraction of a point with the mass of the entire earth, Me, located at the center of the earth, a distance, Re, from the surface of the earth. This nominal gravity value, g=G×Me/Re2, is about 9.8 m/s2. Thus, the freefall acceleration due to gravity near the earth's surface of an object having a small mass compared to the mass of the earth is about 9.8 m/s2. An instrument used to measure gravity is called a “gravimeter.”
The most accurate gravimeters are interferometric absolute gravimeters. The typical interferometric absolute gravimeter uses a freely falling test mass and a laser or single-frequency light beam which reflects from the freefalling test mass. The path length of the reflected beam changes as the test mass tree falls. The reflected light beam is combined with a reference light beam to develop interference fringes. Interference fringes are instances where the amplitude or intensity of the reflected and reference light beams add together to create increased intensity, separated by instances where the two beams cancel or create diminished intensity. Since the freefall movement of the test mass is established by gravity, the occurrence and timing of the resulting interference fringes defines the characteristic of gravity. The use of optical fringe interferometry to measure gravity characteristics is well-known and is described in U.S. Pat. No. 5,351,122.
Fringes occur on a periodic basis depending upon the change in the optical path length of the reflected beam relative to the optical path length of the reference beam. One fringe occurs whenever the optical path difference between the reflected and reference beams changes by the wavelength of the light of the two beams. Movement of the test mass typically changes the beam path length by twice the amount of its physical movement because the physical movement changes both the entry path and exit path of the reflected beam path. In this circumstance, a fringe typically occurs when the object moves by one-half of a wavelength.
A gradient of gravity is the rate at which gravity changes in a certain direction and over a certain distance. A gravity gradient is therefore the change or first derivative of the gravity over distance. An instrument used to measure a gradient of gravity is called a “gradiometer.”
Near-field variations or gradients in gravity are caused by localized variations in the mass or density of at least one of the two attracted bodies. For example, gravity gradients are used to establish the location of underground geological structures, such as a pool of liquid petroleum encased within an earth formation, narrow seams or “tubes” of high density geological materials such as diamonds or cobalt, or voids in a geographical formation caused by a tunnel or cavern. These changes in the subterranean material density are most measurable within a relatively short near-field distance, typically within a few hundred meters.
Subsurface density anomalies, for example from valuable nearby high density ore bodies or voids caused by tunnels or areas of low density material, affect the local value of gravity, g, at a level of about 1 part per million ( 1/106), and in some cases 1 part per billion ( 1/109). The large background of the earth's gravity requires that any direct gravity measurement to detect such subsurface anomalies have a very large dynamic range of parts per billion, otherwise direct gravity measurements will not be useful for locating and detecting such subsurface density anomalies. It is difficult to make gravimeters with such levels of extremely high precision. On the other hand, gradiometers cancel the large effect of the earth's gravity while preserving the ability to detect variations in nearby density anomalies. A gradiometer can have 3×105 times less precision than a gravimeter and still be used effectively to detect or locate nearby mass or density anomalies.
From a logical standpoint, the measurement of a gravity gradient (γ) is obtained by measuring the gravity values (g) at the different locations, subtracting the gravity measurements, and dividing the result by the distance (d) between the locations, i.e. γ=(g2−g1)/z. This quantity is referred to mathematically as the spatial derivative of gravity in the vertical direction. From a practical standpoint, this approach requires a relatively complex mathematical interferometric analysis of the fringes to obtain the gravity values at each location.
Another approach, also from a logical standpoint, is to interferometrically combine the light beam from one gravity measurement with the light beam from the other gravity measurement to create fringes. The number of fringes represents the gradient or differential in gravity. The practical difficulty with this approach is that the difference in the number of fringes is typically in the neighborhood of no more than one fringe, when the test masses move over a distance which can be accommodated by a reasonably sized commercial product. Obtaining an accurate value of the gravity gradient when that value is represented by a single fringe or less than one fringe is very difficult or impossible. The extent of mathematical processing required is extensive and complex, and the accuracy is compromised.
One approach to creating more than one fringe when measuring the gradient of gravity, is to impart a velocity difference between the two freefalling test masses. The test mass with the higher velocity will move a greater distance during freefall than the test mass with the lesser velocity, causing the reflected light beam to traverse a longer beam path. Because the number of fringes generated is related to the difference in the path lengths of the beams, the greater relative difference in the distance of test mass movement results in more fringes. The greater number of fringes makes the interferometric calculation more reliable and accurate, but nevertheless adds complexity to the mathematical calculations.
The size of the gradiometer instrument required to impart an initial velocity difference between the two freefalling test masses is increased, because of the necessity to accommodate the greater freefall distance of the faster moving test mass. Furthermore, the equipment required to impart the initial velocity difference is more complex, as our the requirements for determining when both test masses commence simultaneous freefall. These practical operational requirements, plus the added complexity in interferometric analysis and calculation, adds to the complexity of previous interferometric gradiometers.